Electrical and acoustic borehole-imaging tools are widely used to log subsurface boreholes to locate and map the boundaries between rock layers (i.e., bed boundaries), and to visualize and orient fractures and faults
Electrical borehole images run in water-based mud, such as Schlumberger's FMI (Formation MicroImager) log, are based on dipmeter technology that has been commercially available since the 1950's (Bigelow, 1985a, b, c, d, e; Gilreath, 1987; Adams et al., 1987; Hurley, 2004). FIG. 1 is an illustration of the tool configuration and basic principles behind dipmeter logs. Electrical borehole-imaging tools are, in essence, sophisticated dipmeters. The imaging tools have micro resistivity electrodes arranged around the wellbore on pads that are pressed against the borehole wall. The evolutionary trend from dipmeters to borehole images has been from a few electrodes to complex arrays of electrodes on multiple pads (between 4 to 6 pads, with or without flaps).
The data acquisition sequence for these tools generally runs as follows. Tools are first run into the hole with the pads closed. At the start of the log run, either four, six, or eight pads are pressed against the borehole wall. The number of pads depends on the logging device which is being used. Electrical current is forced into the rock through the electrodes, and remote sensors measure the current after it interacts with the formation (FIG. 2). Raw data include multiple electrode readings, calliper readings from individual pads or pairs of pads, and x-, y-, and z-axis accelerometer and magnetometer readings. Borehole deviation and the first pad (pad 1 for the tool) orientation are determined from the magnetometers. The sample rate for electrode and accelerometer data can be high, of the order of 120 samples/ft (400 samples/m).
Areal coverage of the borehole face is a function of width of the electrode arrays, number of pads, and borehole diameter. In general, 40 to 80% of the borehole face is imaged in typical boreholes. Non-imaged parts of the borehole appear as blank strips between the pads on the resulting borehole log.
Depth of investigation is small, generally less than 1 in (2.5 cm) into the formation (Williams, C. G., Jackson, P. D., Lovell, M. A., and Harvey, P. K., 1997, Assessment and interpretation of electrical borehole images using numerical simulations: The Log Analyst, v. 38, No. 6, p. 34-44). Logging rate, which is comparable to other openhole logs, is 1,600 to 1,800 ft/hr (500 to 550 m/hr). Pressure and temperature limitations are comparable to those placed on conventional logging tools.
Typically, a processed electrical borehole image is basically a map of resistivity of the rock-fluid system at the borehole face. Because it is more difficult to examine borehole images in 3-D, it is common to split the borehole along true north, then unroll the cylinder until it becomes a 2-D view. FIG. 3 represents the schematic diagram of a vertical, cylindrical borehole intersected by a planar feature such as a steeply dipping fracture. The intersection between the plane and the cylinder is either a circle or an oval. To view the borehole in two dimensions, the cylinder is generally cut along a line with an azimuth of true north (N). When the cylinder is flattened, the line of intersection of an oval trace becomes a sinusoidal curve. In highly deviated and horizontal wells, it is common to split the borehole image along the top of the hole. Planar features that intersect the cylindrical borehole appear as sine waves in the 2-D view.
Data processing is done on workstation, PC, or mainframe computers using commercially available software. Processing steps involve correcting the directional data, that is, first pad (pad 1) azimuth (tool orientation) and hole azimuth, for magnetic declination. Some programs also correct for magnetic inclination. Note that magnetic declination varies with time and space. Charts and computer programs are available to compute magnetic declination for any location in the world on any logging date. Next, accelerometer corrections are applied, making sure that the accelerometer curve is depth matched with the resistivity traces. The accelerometer accounts for differential sticking, speed variations, and resonant vibrations that occur as the tool moves up the hole. Finally, resistivity traces must be depth shifted using physical tool specifications, so that different rows of buttons are in line where the same slice of the borehole, perpendicular to the tool, was imaged. At very small scales (less than 6 in; 15 cm), nonlinear depth shifts occur that may not be correctable by conventional data-processing algorithms. As a result, not every surface that shows electrical contrast is exactly on depth.
Typically, borehole images are created by assigning colour maps to different bins or ranges of resistivity values. Colour pixels are then arranged in their proper geometric position around the wellbore. By convention, low-resistivity features, such as shales or fluid-filled fractures, are displayed as dark colours. High-resistivity features, such as sandstones and limestones, are displayed as shades of brown, yellow, and white (FIG. 4, representing small-scale fault, or microfault (M), and bed boundaries (B) in a sand and shale interval). Note the images can also be on gray scale wherein black corresponds to low resistivity and white to high resistivity. The shales occur in the lower part of the section. Examples for creating borehole images can be found in U.S. Pat. Nos. 3,406,776, 4,567,759 and 5,200,705.
Two main types of processed borehole images are available: static and dynamic. Static images are those which have had one contrast setting applied to the entire well. They provide useful views of relative changes in rock resistivity throughout the borehole. Static images can be calibrated in ohm-m to devices such as the Schlumberger's LLS log(Shallow Latero-log), a shallow-reading resistivity log. With normal processing, borehole images are uncalibrated. Images can be corrected for EMEX voltage, a background voltage that is adjusted on the logging truck to improve image quality. Dynamic images, which have had variable contrast applied in a moving window, provide enhanced views of features such as vugs, fractures, and bed boundaries. Dynamic images bring out subtle features in rocks that have very low resistivities, such as shales, and very high resistivities, such as carbonates and crystalline rocks. U.S. Pat. No. 5,809,163, herein incorporated by reference, relates to the analysis of textural features, specifically vugs, using borehole images.
High mud resistivities (greater than 50 ohm-m), typical of oil-based muds, are unsuitable for most electrical borehole images. Since 2001, Schlumberger's OBMI (Oil-Base MicroImager), has been available for oil-based muds. This tool generates borehole images by passing electrical current into the formation from two large electrodes on each pad, which is at a high voltage (about 300V). There is a series of closely spaced buttons, located in two rows of 5 on each of the 4 pads. Borehole images are generated from the potential difference (voltage drop) between the closely spaced electrodes. Wide gaps, corresponding to non-imaged parts of the borehole, are common between pads. This problem can be partially addressed by using 2 passes of the OBMI. An alternative is to use the Dual OBMI, a tool string with 2 OBMI tools mounted adjacent to each other, with the pads of one tool rotated with respect to the other.
Borehole images can be acquired during drilling (LWD, logging-while-drilling). Examples of Schlumberger logging tools are the GVR (GeoVision Resistivity) and ADN (Azimuthal Density Neutron) tools. The GVR uses rotating electrodes, and works in water-based mud. The ADN generates images from azimuthal density readings, and works in any mud. Borehole coverage is complete, with no gaps. However, downward-facing results are generally more reliable because of minimized tool standoff from the borehole wall.
Acoustic borehole images, also known as borehole televiewers, are based on technology first developed in the 1960's (Zemanek, J., Glenn, E. E., Norton, L. J., and Caldwell, R. L., 1970, Formation evaluation by inspection with the borehole televiewer: Geophysics, v. 35, p. 254-269). The UBI (Ultrasonic Borehole Imager) is Schlumberger's primary acoustic tool for open-hole applications. The UBI tool, which is centralized in the well, has a rotating transducer that emits and records sound waves that bounce off of the borehole wall. Both acoustic amplitude and travel time are recorded and processed into images. Normally, borehole coverage is 100%, with no gaps in the images. However, poor-quality images may result when the tool is decentralized, or the borehole wall is irregular.
Therefore, as discussed above, because electrical logging tools are pad-type devices with fixed arrays of electrodes, it is common to have gaps with missing information between the pads. Electrical and acoustic logs commonly have intervals with poor data quality due to non-functioning electrodes, insufficient pad pressure, borehole irregularities, rock debris, decentralized tools, and poor acoustic reflections.
Geostatistics is a discipline concerned with spatially distributed random variables (also called “regionalized variables”), usually applied to problems in the earth sciences, such as estimation of mineral reserves and delineation of mineral deposits, hydrocarbon reservoirs, and groundwater aquifers. Typically it makes use of two-point statistics summarized in a variogram. Multipoint (or multiple-point) geostatistics (MPS) differs from the rest of variogram-based geostatistics primarily in that it characterizes spatial variability using patterns (sets of points) that involve higher order (much greater than order 2) statistics.
Multipoint geostatistical methods have been demonstrated to be computationally feasible and have been tested on real datasets as set forth in i) Strebelle, “Conditional simulation of complex geological structures using multiple-point statistics”, Mathematical Geology, v. 34, n. 1, 2002, pp. 1-22, ii) Strebelle et al., “Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics,” SPE Journal, Vol. 8, No. 3, 2003, pp. 227-235, and iii) Liu et al., “Multiple-point simulation integrating wells, three-dimensional seismic data, and geology,” American Association of Petroleum Geologists Bulletin v. 88, no. 7, 2004, pp. 905-921.
Multipoint geostatistical methods use a numerical training image to represent the spatial variability of geological information. The training image provides a conceptual quantitative description of the subsurface geological heterogeneity, containing possibly complex multipoint patterns of geological heterogeneity. Multipoint statistics conditional simulation anchors these patterns to well data (and/or outcrop data) and to the seismic-derived information (and/or probability field information or constraint grid(s)). An example of such method is described in US-2007-0014435, assigned to Schlumberger Technology Corporation.
Geostatistics relies on the well-known concept of random variables. In simple terms, continuous or discrete properties at various spatial locations are largely unknown or uncertain; hence each property of interest at each spatial location is figured into a random variable whose variability is described by a probability function. In order to perform any type of geostatistical simulation, one requires a decision or assumption of stationarity. In multipoint geostatistical methods, the use of training images is bound by the principle of stationarity as described by Caers, J., and T. Zhang, 2004, “Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models”, in M. Grammer, P. M. Harris, and G. P. Eberli, eds., Integration of Outcrop and Modern Analogs in Reservoir Modeling, Memoir 80: Tulsa, Okla., AAPG. A random spatial field is said to be stationary if all of its statistical parameters are independent of location (invariant according to any translation). In the case of training images, this stationarity can consist of, but is not limited to, orientation stationarity, where directional elements do not rotate across the training image; and scale stationarity (where the size of elements on the image does not change across the training image).
One multipoint geostatistics method is well known in academia and industry by the name of “Single Normal Equation Simulation” (SNESIM) (Strebelle, S., 2000, “Sequential simulation drawing structures from training images, PhD thesis, Stanford University, 200p). The SNESIM method is generally considered useful for practical applications such as modeling categorical or discrete data types, especially for categorical data in 3D property modeling. In the SNESIM method, the conditional probability density function of all categories at one point is computed using knowledge of the value at a number of nearby points and statistics provided by the training image. SNESIM works with discrete values only (i.e., a finite and usually small number of categories, such as for example five different rock types).
Such methodology was well known in the early 1990's (before it was known as “SNESIM”) (Guardiano, F., and R. M. Srivastava, 1993, Multivariate geostatistics: beyond bivariate moments, in A. Soares, ed., Geostatistics-Troia, v. 1: Dordrecht, Netherlands, Kluwer Academic Publications, p. 133-144). One of the limitations of the first MPS approach, however, was that it was extremely computationally intensive to consult the training image multiple times. In 2000, Strebelle developed a technique to store the information contained in the training image in a special tree-like structure that reduced computations enormously (Strebelle, S., 2000, Sequential simulation drawing structure from training images: PhD Thesis, Stanford University, Stanford, Calif., USA). With this improvement, the methodology was commonly referred to as the SNESIM method.
The SNESIM code is faster than Guardiano and Srivastava's (1993) original algorithm, but it is computer random-access memory (RAM) demanding, especially in 3D for a large training image. This RAM limitation in 3D requires compromises that may lead to inadequate shape reproduction of 3D objects. The RAM limitation also prevents from considering too many categories or classes jointly, thus limiting SNESIM to the simulation of categorical variables. The SNESIM algorithm searches for exact replicates of the conditioning data event, builds the reservoir model one pixel at a time, conditioned to a multiple-point data event, and does not allow any filtering or averaging of the patterns found in the training image.
In order to deal with both categorical and continuous variable training images and reduce RAM cost and improve shape reproduction in 3D applications, a new MPS algorithm named FILTERSIM (FILTER-based SIMulation) was proposed by Zhang and described and incorporated herein in Zhang et al. (Zhang T., Switzer P., and Journel A., 2006, Filter-based classification of training image patterns for spatial pattern simulation: Mathematical Geology, v. 38, p. 63-80). The FILTERSIM algorithm applies a set of local filters to the training image, which can be either categorical or continuous, to group local patterns into pattern classes. It then proceeds to simulate patterns on the basis of that classification. A filter is a local template (window) with a set of weights associated to each pixel location of the template. Applying a filter to a local pattern results in a filter score, the score is viewed as a numerical summary of that local pattern. A set of default or use-defined filters is designed such that each filter can record different aspects of the training pattern seen within the template. These filters are used to transform training patterns into a filter score space. This pattern scoring provides a remarkable dimension reduction of patterns. By partitioning that score space of limited dimension, similar training patterns are classified based on their filter scores.
The FILTERSIM algorithm starts with a classification of local training patterns in a filter score space of reduced dimension. Simulation proceeds along a sequential path through the simulation space, by determining which pattern class is most similar to the local conditioning data event, sampling a specific pattern from the pattern class, and then patching the sampled pattern onto the image at the simulation sites. The simulation random path and the sampling of patterns from pattern classes allow for different simulated realizations, yet all are conditional to the same original data. Because of the dimension reduction brought by the filter summaries of any pattern, and because patterns are grouped into classes, the algorithm is fast and reasonable in terms of RAM demand.
The SNESIM and FILTERSIM algorithms are able to honour absolute or so-called “hard” constraints from data acquired in wells or outcrops, and conditional or “soft” constraints from seismic data, facies probability fields, and rotation and affinity (or scale) constraint grids. All of these data are used in the stochastic modeling process to generate 1D, 2D, or 3D maps of geological facies or rock properties. Because there is a random component involved in MPS simulations, individual realizations of property fields created by MPS algorithms differ, but the ensemble of realizations provides geoscientists and reservoir engineers with improved quantitative estimates of the spatial distribution and uncertainty of geological facies in a modeled reservoir volume. Moreover, these algorithms honour both hard and soft input data constraints.
Directional 2D default colour filter may then be used according to the FILTERSIM algorithm (see an example in FIG. 5, showing 6 directional 2D filters wherein the 1st and 2nd filters are average filters; 3rd and 4th are gradient filters; the 5th and 6th are curvature filters). There are three types of filters: average filter, gradient filter and curvature filter, and each type of filter is used for both horizontal and vertical directions. Average filters aim at localizing features; gradient filters are used to detect feature boundaries by highlighting the contrast of different features (the first-order difference); curvature filters supply the second-order difference of features.
FIG. 6 is a flowchart that summarizes the process involved in FILTERSIM simulations. In order to reflect large-scale structure, multi-grid simulation is used, which progressively simulates each level of the multi-grid from coarser to finer with the finer-grid simulation being constrained by previously simulated values at coarser grids. At each level of the simulation, rescaled filters are applied over the respective grid.
There are two types of training images: one with a very limited number of categories and another for continuous variables such as reservoir petrophysical properties. Multipoint geostatistical methods require 1D, 2D, or 3D grids of training images as prior conceptual geological models that contain patterns of the spatial attributes under study. The shapes of different features appearing on the images are supposed to represent a model of real geological features, with each category typically representing a different geological facies or different kind of geological body. Training images are typically required to contain “stationary” patterns, i.e., the patterns must be independent of their location in space (invariant according to any translation) and must be repetitive over the training image area. In the case of training images used for geological modeling, this stationarity can consist, but is not limited to, geological object orientation stationarity (where directional objects/features do not rotate across the image) and geological scale stationarity (where the size of objects/features on the image does not change across the image) (Caers, J. and Zhang, T., 2004, Multiple-point geostatistics: A quantitative vehicle for integration of geologic analogs into multiple reservoir models, in M. Grammer, P. M. Harris and G. P. Eberli, eds.: Integration of Outcrop and Modern Analogs in Reservoir Modeling, AAPG. Memoir 80, p. 383-394).
An issue raised implicitly by current MPS algorithms is how to generate training images. Training images are supposed to model or reproduce real geological features and should as much as possible be derived from existing geologically meaningful images. This requires research on statistical and image-processing methods that will allow use of images from any source, e.g., hand-drawn sketches, aerial photographs, satellite images, seismic volumes, geological object models, physical scale models, or forward geological process models. Compared to the creation of continuously variable training images, generating categorically variable training images is easier. An object-based approach is commonly used to generate training images with categorical variables. A region-based approach, combined with adding desired constraints, can be used to generate continuously variable training images.
In particular, Multipoint geostatistics (MPS) is a new advanced geostatistics approach. It allows reservoir modelers to incorporate their prior knowledge, interpretations, or conceptual models into the reservoir modeling process through training images. These training images are numerical representations of the structures/features that are believed to exist in the reservoir under study. Once we have the training images, MPS can extract curvilinear structures or complex features from the training images and anchor them to the reservoir locations where the samples/observations are collected, leading to more realistic reservoir models. Introducing training images into reservoir modeling is a milestone. Note that there are two ingredients in the use of MPS: training images (conceptual models) and the real data (observations). These two pieces are typically separated.
However, in realistic applications, generating representative training images, in particular in 3D, has proved to be a bottleneck in MPS applications. Generating a continuous variable training image is even more difficult than the creation of categorical training image.